A New Exact Bit-Parallel Algorithm for SAT

Segundo, Pablo San; Tapia, Cristóbal; Puente, Juan Antonio de la; Rodríguez-Losada, D.

doi:10.1109/ictai.2008.127

Cited by 3 publications

(3 citation statements)

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“…Esta biblioteca está accesible al dominio público en [74] En nuestro trabajo su uso se justifica plenamente, puesto que gran parte de los procesos a realizar tratan datos booleanos, y muchos, sobre los cuales se aplican muchas operaciones de tipo lógico, véase por ejemplo [58].…”

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Diseño e implementación de un planificador para un agente autónomo

García¹

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“…Como solvers internos se emplearon miniSAT y un SAT solver desarrollado por el grupo de investigación. Este solver se expuso en un congreso en 2008 [58].…”

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Diseño e implementación de un planificador para un agente autónomo

García¹

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“…Bit parallelism has been successfully used in many computational algorithms, particularly for string matching [27,31,32]. Recently, bit parallelism has been employed for solving hard combinatorial problems, such as SAT [66] and the Maximum Clique Problem [65].…”

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confidence: 99%

Graph-theoretic studies of combinatorial optimization problems

Nokandeh¹,

Mohammad²

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Leonhard Euler introduced the concept of Graph Theory in his paper about the seven bridges of Konigsberg published in 1736. It is the study of pair-wise relationships between objects. Each object is represented using a vertex, and in case of a relationship between a pair of vertices, they will be connected using an edge.In this dissertation, graph theory is used to study several important combinatorial optimization problems. In chapter 2, we study the multi-dimensional assignment problem using its underlying hypergraphs. It will be shown how the MAP can be represented by a k-partite graph and how any solution to MAP is associated to a k-clique in the respective k-partite graph. Two heuristics are proposed to solve the MAP and computational studies are performed to compare the performance of the proposed methods with exact solutions. On the heels of chapter 2, a new branch-and-bound method is proposed to solve the problem of finding all k-cliques in a k-partite graph in chapter 3. The new method utilizes bitsets as the datastructure to represent graph data. A new pruning method is introduced in BitCLQ, and CPU instructions are used to improve the performance of the branch-and-bound method. BitCLQ gains up to 300% speed up over existing methods. In chapter 4, two new heuristics to solve decomposable cost MAP's are proposed. The proposed heuristic are based on the partitioning of the underlying graph representing the MAP. In the first heuristic method, MAP's are partitioned into several smaller MAP's with the same dimensial-2 ity and smaller cardinality. The second heuristic works in the same fashion. But instead of partitioning the graph along the elements, graphs are divided into smaller graphs with the same cardinality but smaller dimensionality. The heuristics are then used in exact branch and bound methods and numerical comparison of the resulting method is provided. Maximum Clique problem entails finding the size of the largest clique contained in a graph. General branch-and-bound methods to solve MCQ use graph coloring to find an upper bound on the size of the maximum clique. In chapter 5, a branch and bound algorithm is proposed for the maximum clique problem. that is based on the method of 5. Chapter 6 contains an application of a graph theory in solving a risk management problem. The mixed-integer mathematical model to formulate a risk-based network is provided. It will be shown that an optimal solution of the model is a maximal clique in the underlying graph representing the network. Abstract Approved: Thesis SupervisorABSTRACT Leonhard Euler introduced the concept of Graph Theory in his paper about the seven bridges of Konigsberg published in 1736. It is the study of pair-wise relationships between objects. Each object is represented using a vertex, and in case of a relationship between a pair of vertices, they will be connected using an edge.In this dissertation, graph theory is used to study several important combinatorial optimization problems. In chapter 2, we study the multi-dimensional assignment p...

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On finding k-cliques in k-partite graphs

Mirghorbani

Krokhmal

2012

Optim Lett

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A New Exact Bit-Parallel Algorithm for SAT

Cited by 3 publications

References 14 publications

Diseño e implementación de un planificador para un agente autónomo

Diseño e implementación de un planificador para un agente autónomo

Graph-theoretic studies of combinatorial optimization problems

On finding k-cliques in k-partite graphs

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